The Apple-owned music recognition app, Shazam, has a Wear OS app, and it recently received a huge update (via 9To5Google) for Wear OS-based smartwatches. You can install it on your Galaxy Watch 4 (or newer) if want to recognize music playing around you or want to discover new new songs.
The newest version of the Shazam app now operates independently of the phone app. Earlier, it would require the paired phone in the watch's wireless range. This is a great improvement, as you can use the app even when you're not carrying your phone with you. Moreover, earlier, the app would start listening to music as soon as you launched the app. Now, you have to click on the Shazam logo to start the music recognition process.
Even when your watch is not connected to the internet, the Shazam app can recognize music when the watch is connected to the internet. What it does is, it records the music that needs to be recognized, and then analyzes it when the watch is connected to the internet. Identified songs are instantly synced to all other devices where you have your Shazam app logged in.
When you scroll down from the app's main screen, it displays the list of the songs you asked to be recognized earlier. When any song is recognized, its title, album, and artist details are displayed. You can now install the new version of Shazam from the Play Store on your phone or your Galaxy Watch.